The overall goal of this proposal is to characterize and differentiate the effects of population mixtures from that of genetic linkage and past demographic changes, so that such effects can be taken into account for purposes of gene mapping, studying evolutionary history, and forensic genetics. Using the theory of coalescence and diffusion models, we propose to develop a unified measure of linkage disequilibrium (LD) that maintains a monotone relationship with recombination distance of markers for repeat loci as well as single nucleotide polymorphisms (SNPs). The effects of past demographic changes of population size on multi-point LD will be studied for repeat loci that evolve via a general stepwise mutation process (with asymmetry allowed). We shall also develop methods for examining the effect of allele size constraints and expansion/contraction mutation bias on inference of the consequences of genetic linkage versus mixture of populations. This will allow a characterization of the distinction between multi-point LD generated by population mixture versus genetic linkage. In addition, new laboratory data on PCR-based DNA polymorphisms on selected mixed populations (African-Americans, US Hispanics, Mexicans from Nuevo Leon, and admixed Uruguayans of northeastern Uruguay) will be generated to obtain precise estimates of admixture in these populations by using newly developed population-specific markers, and to evaluate the effects of sex-specific differential gene flow from parental populations by using mitochondrial and Y-chromosome haplotypes. Such data, in addition to the models of the effects of directional mating, will set precise bounds for relevant parameters under which mixed populations can be used for genetic linkage studies. The results of this project will aid (a) in assessing the utility of populations of different mixture history in developing strategies for mapping genes using repeat markers, and (b) in understanding the history of mutations at genes underlying complex diseases.